See this post on the official Mozilla forums for the solution for today's Thunderbird. In summary, download the Thunderbird DMG that's linked in the first post there, launch it, and make some relatively easy configuration changes to add Address Book support.
To make the configuration changes, you need to open the Config Editor -- open Thunderbird' Preferences, click Advanced, then on the General tab, click the Config Editor button. Control click on the list of values and select New, and add three keys:
- ldap_2.servers.osx.description (string) with a value of OS X
- ldap_2.servers.osx.dirType (integer) with a value of 3
- ldap_2.servers.osx.uri (string) with a value of moz-abOSXdirectory:///
[robg adds: I haven't tested this one.]

